Name: ______________________
Class: __________________
AU6: Notes #4 – Geometric Sequences
Date: __________________
Warm-Up
Use inductive reasoning to describe each pattern, and then find the next two numbers in each
pattern. If the sequence is arithmetic, write the function for the sequence.
2,
5,
8,
11,
_______,
_______
3,
12,
48,
192,
_______,
_______
Another kind of number sequence is a geometric sequence. You form a geometric sequence by
multiplying a fixed number to each previous term; this fixed number is called the common ratio.
Example 1 – Finding Common Ratio and the next two terms in the sequence
A)
2,
4,
8,
16,
_______,
_______
B)
80,
20,
5,
5
,
4
_______,
_______
1
Try-It!
Determine the common ratio and the next two terms of the sequence.
A)
3,
9,
27,
81,
_______,
_______
B)
2,
-6,
18,
-54,
_______,
_______
C)
750,
150,
30,
6,
_______,
_______
Example 2: Writing a Function Rule for a Geometric Sequence
Consider the sequence 2, 6, 18, 54,… think of each term as the output of a function. Think of
the term number as the input.
Term number: 1
2
3
4
 input
Term:
6
18
54
output
2
Let: n = the term number in the sequence
An  value of the nth term of the sequence
An
n
1
2
2
2
2
2x3
2 x 31
6
3
2x3x3
2 x 32
18
4
2x3x3x3
2 x 3__
54
n
2x3x3…x3
2 x 3(
The general form of a geometric sequence
2
)
A(n)  a  b n 1
Try-It!
Write the function rule for the geometric sequence.
A)
2,
8,
32,
128
B)
-80,
20,
-5,
1.25
Example 4 – Finding Terms of a Sequence
Find the first, second, and twelfth terms of the sequence.
Given: A(n)  5  2
n 1
Try-It!
Find the first, second, and twelfth terms of the sequence.
A)
A(n)  5 (2) n 1
1
A(n)  20   
5
B)
n 1
C) Suppose you bounce a ball to a height of 100cm and it continues to bounce to lower and
lower heights. Each bounce only comes up to 80% of the previous height. Write a function rule
for the height of the ball after n, bounces. How high will the ball reach after the eleventh bounce?
3